• Alternative model structures are proposed that include an inhibiting dependency on either ammonium or phosphate or both in the product formation.
• Alternative model structures will neglect a direct limiting dependency of the compartment building-up reactions on ammonium or phosphate. However, al-ternative model structure are proposed that consider a precursor (intermediate compartment) for both protein and DNA/RNA which is built up on phosphate.
• Simple relationships between DNA, RNA, and proteins like limiting or inhibiting dependencies cannot be found and will therefore not be considered in any model structure, i.e., Eq. (6.4) will not be extended by limiting or inhibiting kinetic expressions with respect to these compartments.
• A relationship between the product and DNA, RNA, or the proteins cannot be found either, i.e., rP is independent of these compartments.
The six most likely model structures are considered to find suitable model candidates.
Again, the ‘limit’ terms in the reaction network are substituted for the Michaelis–
Menten law and the ‘inhib’ term is replaced with the Jerusalimski–Engamberdiev law.
DNA, RNA, proteins and the remaining biomass Xr are regarded as possible options for Ckin the building-up reactionrXr (6.4). To calculate the compartment degradation rates rdCi, both Eqs. (6.6) and (6.27) are tested. This leads to 152 model candidates.
The parameters and the experiment-related initial values of the compartments are identified based on four experimental runs. Finally, the models are ordered by their AICc values.
The simulations of the 10 best identified models are compared to real data in Fig-ure 8.7. For the other identified experiments, see Appendix C.5. As can be seen, many of the simulations barely differ from each other and can explain most of the measurements equally well. However, the models are not able to mimic the phosphate consumption correctly. This becomes obvious when phosphate is depleted in the ex-periments and it starts being fed. In the simulations, the phosphate concentration increases whereas it cannot be measured in the experiments.
Subsequently, two experimental runs—not used for the identification—are used for val-idation, where the initial values of the cell-intern states are estimated. In Figure 8.8, the comparison between the predictions and the actual measurements can be seen.
The second experiment is given in Appendix C.6. It is obvious that some dynamic aspects in the reaction network are yet to be considered by the model candidates. In addition to the aformentioned shortcomings regarding phosphate, DNA and nikko-mycin measurements show some characteristics, as well, that cannot be described by the simulations. However, the models are able to explain the dynamic of the other measurements well.
Unfortunately, further experiments to improve the model quality cannot be conducted as the strain used,S. tendaeTü 901/8c, had over the years lost its capability to produce nikkomycin. Therefore, new data could not be compared to the old data used here.
8.2 Streptomyces tendae
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Figure 8.7: Identified experiment STdef2 for S. tendae. The simulations based on the 10 best identified model candidates are shown as solid lines, circles indicate the measurements. The feeding rates are the result of an on-line trajectory planning.
Automated detection of model deficiencies
The best validated model is tested for model deficiencies. The two most important differences between the measurements and simulations are listed below.
• Based on the measurements, the phenomenon DNA formation limited by am-monium is rejected with Sc = −0.50, whereas the simulations accept it with Sc= 0.50.
• The same applies to the phenomenon protein formation limited by ammonium.
To account for these deficiencies, the simplest approach is to eliminate the limiting effect of ammonium in both rD(t) and rPr(t). However, since both phenomena are rejected by the measurements, model structures already exist that neglect those influ-ences and do not perform better than the best model. Moreover, since the additionally added compartments D∗ and Pr∗ are not built up on ammonium—the
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Figure 8.8: Validation experiment STdef3 forS. tendaeusing as well the 10 best model candidates
inherent phenomena do not show such relationships—DNA and the proteins are not built up on ammonium at all. Taking the biological knowledge (see Section 2.2) into account, this does not make any sense. Therefore, the simplest approach is not used to improve the model. Instead, other modifications are tried.
In Figure 8.9(a), the relevant part of the biological network of the best validated model can be seen. Two model candidates (Figure 8.9(b) and 8.9(c)) try to account for the false detection of the ammonium-limited DNA formation. Here, different combina-tions of Eqs. (8.1)–(8.3) are manually changed. For example, model STBVb neglects the limiting influence of ammonium in the DNA building-up reaction rD(t) and adds ammonium in the formation of D∗. Additionally to these changes, model STBVc eliminates a direct mass flow from ammonium to DNA by modifying Eq. (8.1). Cor-respondingly, two models (Figure 8.9(d) and 8.9(e)) try to compensate for the false detection of the ammonium-limited protein formation. At last, two models are man-ually generated that try to account for both shortcomings and are a combination of the aforementioned models.
8.2 Streptomyces tendae
Am + Ph + Gc−→rD D (8.1)
rD=rD(cAm(t)) (8.2)
Ph→D∗ →D (8.3)
Am + Ph + Gc−→rPr Pr (8.4)
rPr=rPr(cAm(t)) (8.5)
Ph→Pr∗ →Pr (8.6)
(a) Best validated model STBV
rD6=rD(cAm(t)) (8.2b) Am + Ph→D∗→D (8.3b) (b) Modifications for model STBVb
Ph + Gc−→rD D (8.1c) rD6=rD(cAm(t)) (8.2c) Am + Ph→D∗ →D (8.3c) (c) Modifications for model STBVc
rPr6=rPr(cAm(t)) (8.5d) Am + Ph→D∗→D (8.6d) (d) Modifications for model STBVd
Ph + Gc−→rPr Pr (8.4e) rPr6=rPr(cAm(t)) (8.5e) Am + Ph→D∗ →D (8.6e) (e) Modifications for model STBVe
rD6=rD(cAm(t)) (8.2f) Am + Ph→D∗ →D (8.3f) rPr6=rPr(cAm(t)) (8.5f) Am + Ph→D∗ →D (8.6f) (f) Modifications for model STBVf
Ph + Gc−→rD D (8.1g) rD6=rD(cAm(t)) (8.2g) Am + Ph→D∗ →D (8.3g) Ph + Gc−→rPr Pr (8.4g) rPr6=rPr(cAm(t)) (8.5g) Am + Ph→D∗ →D (8.6g) (g) Modifications for model STBVg
Figure 8.9: Modifications to the best validated model of S. tendae to account for de-tected deficiencies. (a) Relevant excerpt from the biological network of the best validated model. (b)–(g) Different modifications that lead to six alternative model candidates.
These six model candidates are subjected to a parameter identification step and a validation step, using the same identification and validation experiments as mentioned above. Unfortunately, the models do not describe the measurements better.